Non-paraxial effects on laser-qubit operations

TL;DR

This paper investigates how non-paraxial effects in tightly-focused laser beams influence quantum operations in atomic systems, revealing potential sources of error and guiding high-precision quantum control.

Contribution

The authors develop an analytic and numerical framework to quantify non-paraxial effects on laser-driven qubit operations, extending beyond the paraxial approximation.

Findings

Non-paraxial effects cause spatially-dependent Rabi frequencies and Stark shifts.

These effects lead to qubit-motion coupling and gate infidelities.

Regimes where non-paraxial effects are significant are identified.

Abstract

Tightly-focused laser beams, or optical tweezers, are essential for analogue and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which breaks down at the focus of optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how non-paraxial effects will manifest in the next-generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole $^2$S$_{1/2}\rightarrow$ $^2$D$_{5/2}$ transition in $^{40}$Ca$^+$. Longitudinal field components in the beam center cause spatially-dependent Rabi frequencies and AC Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where non-paraxial effects should be taken into account for high-precision quantum control. Finally, we highlight that non-paraxial effects are potentially more severe in the case of neutral atom and molecule addressing.